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Durham University

Department of Physics

PHYS4241 Theoretical Physics 4 (2018/19)

Details of the module's prerequisites, learning outcomes, assessment and contact hours are given in the official module description in the Faculty Handbook - follow the link above. A detailed description of the module's content is given below, together with book lists and a link to the current library catalogue entries. For an explanation of the library's categorisation system see https://www.dur.ac.uk/physics/students/library/

Content

Relativistic Electrodynamics

Dr J.R. Andersen

18 lectures + 8 workshops in Michaelmas Term

Textbooks:

Required: Modern Electrodynamics, A Zangwill (Cambridge University Press)

[If you have already purchased the book below, then you are not also required to purchase Modern Electrodynamics]

Additional: Introduction to Electrodynamics, D. J. Griffiths (Peason, 3rd Edition)
The course is defined by material contained in this book and in particular the material defined in the syllabus below where the numbers refer to the sections in the book.

Syllabus:

  1. Einsteins postulates [12.1]
  2. The geometry of relativity [12.1]
  3. Lorentz transformations [12.1]
  4. Structure of space-time [12.1]
  5. Proper time and proper velocity [12.2]
  6. Relativistic energy and momentum [12.2]
  7. Relativistic Kinematics [12.2]
  8. Relativistic Dynamics [12.2]
  9. Magnetism as a relativistic phenomena [12.3]
  10. How the Fields transform [12.3]
  11. The Field Tensor [12.3]
  12. Electrodynamics in Tensor notation [12.3]
  13. Relativistic potentials [12.3]
  14. Scalar and Vector potentials [10.1]
  15. Gauge transformations [10.1]
  16. Coulomb gauge [10.1]
  17. Retarded potentials [10.2]
  18. Fields of a moving point charge [10.3]
  19. Dipole radiation [11.1]
  20. Radiation from point charges [11.2]

Quantum Theory 3

Prof V.V. Khoze

18 lectures + 9 workshops in Epiphany Term

Textbooks:

Required: Quantum Mechanics, B. H. Bransden and C. J. Joachain (Prentice Hall, 2nd Edition)
The course is defined by material contained in this book and in particular the material defined in the syllabus below where the numbers refer to the sections in the book.

Syllabus:

  1. Scattering experiments and cross sections [13.1]
  2. Potential scattering (general features) [13.2]
  3. Spherical Bessel functions (application: the bound states of a spherical square well) [7.3 and 7.4]
  4. The method of partial waves (scattering phase shift, scattering length, resonances, applications) [13.3 and 13.4]
  5. The integral equation of potential scattering [13.5]
  6. The Born approximation [13.6]
  7. Collisions between identical particles [13.7]
  8. Introduction to multichannel scattering [13.8]
  9. The density matrix (ensemble averages, the density matrix for a spin-1/2 system and spin-polarization) [14.1, 14.2 and 14.3]
  10. Quantum mechanical ensembles and applications to single-particle systems [14.4 and 14.5]
  11. Systems of non-interacting particles (Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein statistics, ideal Fermi-Dirac and Bose-Einstein gases) [14.6]
  12. The Klein-Gordon equation [15.1]
  13. The Dirac equation [15.2]
  14. Covariant formulation of Dirac theory [15.3]
  15. Plane wave solutions of the Dirac equation [15.4]
  16. Solutions of the Dirac equation for a central potential [15.5]
  17. Negative energy states and hole theory [15.7]
  18. Non-relativistic limit of the Dirac equation [15.6]
  19. Measurements and interpretation (hidden variables, the EPR paradox, Bell’s theorem, the problem of measurement) [17.1 to 17.4]

Revision

2 lectures in Easter Term, one by each lecturer.

Teaching Methods

Lectures: 2 one-hour lectures per week.

Workshops: These provide an opportunity to work through and digest the course material by attempting exercises assisted by direct interaction with the workshop leaders. They also provide opportunity for you to obtain further feedback on the self-assessed formative weekly problems. Students will be divided into four groups, each of which will attend one one-hour class every week. The workshops for this module are not compulsory.

Progress test: One compulsory formative progress test (to be completed over the Christmas break)

Problem exercises: See https://www.dur.ac.uk/physics/students/problems/

Dissertation: Students undertake a dissertation in physics of approximately 1500 words in length. The subject matter is to be chosen with the advice of the course lecturers who will provide a list of suitable topics. The aim should be to pick a topic which has a high physics content appropriate for Level 4, which is accessible to the student and can be readily researched, and which can be discussed satisfactorily within the word count limit. The technical level should be advanced, rather than introductory. Students should discuss with the lecturer the qualities expected in the dissertation, but an indication of these is given in the mark proforma used for assessment. The proforma will be made available to students for their information at the beginning of the Michaelmas Term. The dissertation is summatively assessed. The marked dissertations along with the completed proformas (giving feedback including the marks awarded for the dissertation) will be returned to students before the end of the Epiphany Term.